Robust time-of-arrival source localization employing error covariance of sample mean and sample median in line-of-sight/non-line-of-sight mixture environments

Abstract

We propose a line-of-sight (LOS)/non-line-of-sight (NLOS) mixture source localization algorithm that utilizes the weighted least squares (WLS) method in LOS/NLOS mixture environments, where the weight matrix is determined in the algebraic form. Unless the contamination ratio exceeds 50 %, the asymptotic variance of the sample median can be approximately related to that of the sample mean. Based on this observation, we use the error covariance matrix for the sample mean and median to minimize the weighted squared error (WSE) loss function. The WSE loss function based on the sample median is utilized when statistical testing supports the LOS/NLOS state, while the WSE function using the sample mean is employed when statistical testing indicates that the sensor is in the LOS state. To testify the superiority of the proposed methods, the mean square error (MSE) performances are compared via simulation.

MCC-CKF: A Distance Constrained Kalman Filter Method for Indoor TOA Localization Applications

“…In the literature, such as in [3,10], is is shown that e LOS and e NLOS obey normal distribution, namely e LOS ∼ N (µ LOS , σ 2 LOS ) and e NLOS ∼ N (µ NLOS , σ 2 NLOS ). We use d to denote the true distance between the target node and the reference one.…”

“…For a more detailed discussion of Kalman Filtering, please consult [30]. Therefore, we formulate a a new cost function to better describe the condition with the existence of colored noises, in consideration of the weighting matrices of least squared (LS) method [3,31]. It could be described as follows:…”

“…However, TOA-based ranging and positioning accuracy are affected by multipath and non-line-of-sight (NLOS) scenarios. The error from NLOS [2][3][4] is considered as the most important element affecting the accuracy. Therefore, the research on how to reduce TOA ranging error and improving positioning accuracy has been a long-term concern of the academic world and the industry.…”

Time-of-arrival source localization based on weighted least squares estimator in line-of-sight/non-line-of-sight mixture environments

“…Thus, we employ the WLS algorithm for the LOS/NLOS mixture state, where the error distribution of LOS/NLOS state is not known. Although the WLS estimator in the LOS/NLOS mixture situation was already developed in Park and Chang, 13 the notable difference between the existing WLS and proposed method is that the proposed method does not require the noise variance information unlike the existing WLS algorithm. Also, the proposed method does not need the statistical testing to discern the outliers.…”

Nonlinear programming-based ranging optimization for three-dimensional indoor time of arrival localization

“…The basic indoor TOA positioning algorithms include Taylor series-based estimation, 11,12 geometric relations-based algorithm, 13,14 maximum likelihood estimation, 14,15 and least square (LS). [16][17][18][19] Some improved localization algorithms, which are based on these basic ones, were proposed in the existing literatures to reduce the effect of large ranging error caused by NLOS. LS is one of the most popular algorithms adopted TOA-based indoor positioning due to its low computational complexity.…”